[M19-IMPL-01] Mina Kimchi proof system integration

Description

Integrate Mina's Kimchi proof system for succinct verification in SIP.

Why Kimchi?

• Succinct: Constant-size proofs (~22KB)
• Recursive: Proofs can verify other proofs
• Mina-native: Direct integration path
• Relationship: Zypherpunk hackathon connection

Tasks

• Research Kimchi proof system architecture
• Set up o1js development environment
• Implement SIP circuits in o1js
• Generate Kimchi proofs for shielded transfers
• Benchmark proof generation/verification
• Document integration patterns

Technical Approach

import { Field, Circuit, Proof } from 'o1js'

class ShieldedTransferCircuit extends Circuit {
  @public commitment: Field
  @public nullifier: Field
  
  verify(
    amount: Field,
    blinding: Field,
    spendingKey: Field
  ): Bool {
    // Verify Pedersen commitment
    const expectedCommitment = pedersenHash(amount, blinding)
    commitment.assertEquals(expectedCommitment)
    
    // Verify nullifier
    const expectedNullifier = poseidonHash(commitment, spendingKey)
    nullifier.assertEquals(expectedNullifier)
    
    return Bool(true)
  }
}

Acceptance Criteria

• Kimchi proofs generated for SIP transfers
• Proof size < 25KB
• Verification time < 100ms
• Documentation complete
• Integration tests pass

Parent

• Epic: #825

References

• o1js Documentation
• Kimchi Specification

Start with the linked o1js documentation and Kimchi specification to understand the proof-system architecture and development environment. Then determine how SIP shielded transfers map to the proposed TypeScript circuit and measure proof size and generation and verification times. Done means Kimchi proofs are generated for SIP transfers, meet the stated performance limits, documentation is complete, and integration tests pass.